Newtonian Spaces Based on Quasi-Banach Function Lattices

  • Lukáš Malý

Abstract

In this paper, first-order Sobolev-type spaces on abstract metric measure spaces are defined using the notion of (weak) upper gradients, where the summability of a function and its upper gradient is measured by the "norm" of a quasi-Banach function lattice. This approach gives rise to so-called Newtonian spaces. Tools such as moduli of curve families and Sobolev capacity are developed, which allows us to study basic properties of these spaces. The absolute continuity of Newtonian functions along curves and the completeness of Newtonian spaces in this general setting are established.
Published
2016-08-19
How to Cite
Malý, L. (2016). Newtonian Spaces Based on Quasi-Banach Function Lattices. MATHEMATICA SCANDINAVICA, 119(1), 133-160. https://doi.org/10.7146/math.scand.a-24188
Section
Articles